Answer:y = -3.5x + 9
Explanation:
To find the linear function for the data in the table, we can use the slope-intercept form of a linear equation, which is y = mx + b. In this equation, m represents the slope of the line and b represents the y-intercept.
To determine the slope, we can use two points from the table. Let's choose the points (0, 9) and (1, 5.5). The formula for calculating the slope between two points is given by:
m = (y2 - y1) / (x2 - x1)
Using the coordinates of the two points, we can substitute the values into the formula:
m = (5.5 - 9) / (1 - 0)
m = -3.5
Now that we have the slope, we can substitute it into the slope-intercept form of the linear equation along with the coordinates of one point (0, 9). Let's use (0, 9):
y = mx + b
9 = -3.5(0) + b
9 = b
Therefore, the linear function for the data in the table is:
In this equation, x represents the independent variable (the x-values in the table) and y represents the dependent variable (the y-values in the table).